2024 – An investigator claims with 95 percent confidence that the interval between 10 and 16 miles includes the mean commute

An investigator claims, with 95 percent confidence, that the interval between 10 and 16 miles includes the mean commute distance for all California commuters. To have 95 percent confidence signifies that:
a.
the unknown population mean is definitely between 10 and 16 miles
b.
if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians
c.
if sample means were obtained for a long series of samples, approximately 95 percent of all sample means would be between 10 and 16 miles
d.
the unknown population mean is between 10 and 16 miles with probability .95

Question 2

Any shift to a higher confidence level produces a:
a.
narrower, more precise confidence interval
b.
wider, less precise confidence interval
c.
wider, more precise confidence interval
d.
narrower, less precise confidence interval

Question 3

the larger the sample size,
a.
the larger the standard error and the narrower the confidence interval
b.
the smaller the standard error and the wider the confidence interval
c.
the smaller the standard error and the narrower the confidence interval
d.
the larger the standard error and the wider the confidence interval

Question 4

The t distribution is most different from the standard normal distribution when sample size is:
a.
medium
b.
large
c.
very small
d.
infinitely large

Question 5

A tire manufacturer wishes to show that, on average, a steel-belted radial tire provides more than 50,000 miles of wear. A random sample yields a sample mean of 53,500 and a standard deviation of 5,300 miles. From the manufacturer’s perspective, it would be best of the sample size were:
a.
20
b.
30
c.
40
d.
50

Question 6

Even though the population standard deviation is unknown, an investigator uses z rather than the more appropriate t to test a hypothesis at the .01 level of significance. In this situation the true level of significance of this test is:
1.
smaller than .01
2.
unknown
3.
equal to .01
4.
larger than .01

Question 7

the t test for two independent samples has degrees of freedom equal to the
1.
two sample sizes combined
2.
two sample sizes combined minus one
3.
two sample sizes combined minus two
4.
two sample sizes combined minus three
5.
larger sample

Question 8

The p-value for a test represents the probability
a.
of the observed result, whether the null hypothesis is true or false
b.
of the observed result, given that the null hypothesis is true
c.
that the null hypothesis is true
d.
that the decision is correct 

Question 9

If two independent samples each consists of 20 subjects, a t-test for a difference between their population means will involve how many degrees of freedom?
a.
19
b.
20
c.
38
d.
39
e.
40

Question 10

The general idea behind all of these t-tests is that you are:
a.
only comparing the sample means to the population means, since you don’t know the true variance in the sample or in the population, and the variance doesn’t matter as long as the sample means are different.
b.
comparing within variation to between variation by dividing the chance variation within the samples by the systematic difference between two samples (or between a sample and a population).
c.
comparing between variation to within variation by dividing the systematic difference between two samples, or between a sample and a population, by the chance variation within the samples.
d.
comparing sample variation to population variation by dividing one by the other

Question 11

Given two independent samples with means = 33 and 24, the estimated standard error = 3, and each sample had 5 scores, what is the p-value for: a two-tailed test? a one-tailed test?
a.
two-tailed: p < .01 ; one-tailed: p .05 ; one-tailed: p < .05
c.
two-tailed: p < .05 ; one-tailed: p < .01
d.
two-tailed: p < .01 ; one-tailed: p < .01
e.
two-tailed: p < .05 ; one-tailed: p < .05

11) Given two independent samples with means = 33 and 24, the estimated standard error = 3, and each sample had 5 scores, what is the p-value for: a two-tailed test? a one-tailed test?